How do you find the axis of symmetry, and the maximum or minimum value of the function y = 3x^2 + 24x - 1?

1 Answer
May 30, 2016

3x^2+24x-1 equiv 3(x+4)^2-49

Explanation:

Giving a parabola written as

y = a(x-x_0)^2+b

geometrically speaking we can qualify:

{(x_0 = "axis of symmetry"), (a = "scale factor"), (b = "offset value"):}

Given a parabola such as

y = 3x^2+24x-1

we can reduce it to the former formulation, making

3x^2+24x-1 = a(x-x_0)^2+b

and equating the coefficients, results in

{(-1 - b - a x_0^2 = 0), (24 + 2 a x_0=0), (3 - a=0):}

solving for a,b,x_0

{a = 3, b = -49, x_0 = -4}

and the equivalent formulation

3x^2+24x-1 equiv 3(x+4)^2-49